Algebra Examples

$a \sqrt{b} + \sqrt{a^{2} b} - \sqrt{a b^{3}}$

Step 1

Simplify each term.

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Step 1.1

Pull terms out from under the radical.

$a \sqrt{b} + a \sqrt{b} - \sqrt{a b^{3}}$

Step 1.2

Rewrite $a b^{3}$ as $b^{2} (a b)$ .

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Step 1.2.1

Factor out $b^{2}$ .

$a \sqrt{b} + a \sqrt{b} - \sqrt{a (b^{2} b)}$

Step 1.2.2

Reorder $a$ and $b^{2}$ .

$a \sqrt{b} + a \sqrt{b} - \sqrt{b^{2} a b}$

Step 1.2.3

Add parentheses.

$a \sqrt{b} + a \sqrt{b} - \sqrt{b^{2} (a b)}$

$a \sqrt{b} + a \sqrt{b} - \sqrt{b^{2} (a b)}$

Step 1.3

Pull terms out from under the radical.

$a \sqrt{b} + a \sqrt{b} - b \sqrt{a b}$

$a \sqrt{b} + a \sqrt{b} - b \sqrt{a b}$

Step 2

Add $a \sqrt{b}$ and $a \sqrt{b}$ .

$2 a \sqrt{b} - b \sqrt{a b}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$